10 lines
483 B
TeX
10 lines
483 B
TeX
\section{The Cayley Digraph of a Group}
|
|
|
|
\begin{definition}[Cayley Digraph of a Group]
|
|
Let $G$ be a finite group and let $S$ be a set of generators for $G$. We define a digraph Cay$(S:G)$, called the \textit{Cayley digraph of $G$ with generating set $S$}, as follows.
|
|
\begin{enumerate}
|
|
\item Each element of $G$ is a vertex of Cay$(S:G)$.
|
|
\item For $x$ and $y$ in $G$, there is an arc from $x$ to $y$ if and only if $xs=y$ for some $s \in S$.
|
|
\end{enumerate}
|
|
\end{definition}
|